Final answer:
For a first-order reaction that is 20% complete after one hour, the extent of completion after 3 hours would be more than 20% but less than 60%. The exact value cannot be determined without the rate constant or additional data points.
Step-by-step explanation:
To determine the extent of completion for a first-order reaction after 3 hours, it is important to understand how the percentage completion changes over time for such reactions. For a first-order reaction, the percentage completion increases in a logarithmic fashion, not linearly, due to the rate being proportional to the remaining concentration of reactant.
Given that the reaction is 20% complete in one hour, we can find the first-order half-life from this data. The first-order half-life is the time it takes for half of the reactant to be consumed. If 20% is consumed in one hour, the half-life is greater than one hour since less than half of the reactant has reacted. However, without the specific rate constant (k) for the reaction or additional data points, we cannot precisely calculate the percent completion after 3 hours.
The answer cannot be precisely determined from the given information, but it's important to note that it won't be as simple as doubling the one-hour completion percentage. This is due to the logarithmic nature of first-order reactions, where the rate of reaction decreases as the reactant concentration decreases. So, the percent completion after 3 hours would be less than 60% but more than 20%. Without additional data, we cannot provide an exact answer to the multiple-choice question.